R2Cuba (version 1.1-0)

suave: Integration with SUbregion-Adaptive Vegas Algorithm

Description

Suave uses vegas-like importance sampling combined with a globally adaptive subdivision strategy: Until the requested accuracy is reached, the region with the largest error at the time is bisected in the dimension in which the fluctuations of the integrand are reduced most. The number of new samples in each half is prorated for the fluctuation in that half.

Usage

suave(ndim, ncomp, integrand, ..., lower=rep(0,ndim), upper=rep(1,ndim), rel.tol= 0.001, abs.tol = 0, flags=list(verbose=1, final=1, pseudo.random=0, smooth=0, mersenne.seed=NULL), min.eval=0,  max.eval=50000, nnew=1000, flatness= 50)

Arguments

ndim

same as cuhre

ncomp

same as cuhre

integrand

same as cuhre; But, here, the input argument phw contains the weight of the point being sampled. This extra value can safely be ignored.

...

same as cuhre

lower

same as cuhre

upper

same as cuhre

rel.tol

same as cuhre

abs.tol

same as cuhre

flags

same as cuhre. flags may have an additional component: smooth. When = 0, apply additional smoothing to the importance function, this moderately improves convergence for many integrands. When = 1 , use the importance function without smoothing, this should be chosen if the integrand has sharp edges.

min.eval

same as cuhre

max.eval

same as cuhre

nnew

the number of new integrand evaluations in each subdivision.

flatness

This parameter determines how prominently “outliers”, i.e. individual samples with a large fluctuation, figure in the total fluctuation, which in turn determines how a region is split up. As suggested by its name, flatness should be chosen large for “flat” integrands and small for “volatile” integrands with high peaks. Note that since flatness appears in the exponent, one should not use too large values (say, no more than a few hundred) lest terms be truncated internally to prevent overflow. More details about this parameter can be found Hahn's paper from 2005 and in Cuba documentation.

Value

Idem as cuhre

Details

See details in the documentation.

References

T. Hahn (2005) CUBA-a library for multidimensional numerical integration. Computer Physics Communications, 168, 78-95.

See Also

cuhre, divonne, vegas

Examples

integrand <- function(arg, weight) {
  x <- arg[1]
  y <- arg[2]
  z <- arg[3]
  ff <- sin(x)*cos(y)*exp(z);
return(ff)
} # end integrand
suave(3, 1, integrand, rel.tol=1e-3,  abs.tol=1e-12,
             flags=list(verbose=2, final=0))